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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/defs".
21 include "pc3/defs.ma".
23 inductive ty3 (g: G): C \to (T \to (T \to Prop)) \def
24 | ty3_conv: \forall (c: C).(\forall (t2: T).(\forall (t: T).((ty3 g c t2 t)
25 \to (\forall (u: T).(\forall (t1: T).((ty3 g c u t1) \to ((pc3 c t1 t2) \to
27 | ty3_sort: \forall (c: C).(\forall (m: nat).(ty3 g c (TSort m) (TSort (next
29 | ty3_abbr: \forall (n: nat).(\forall (c: C).(\forall (d: C).(\forall (u:
30 T).((getl n c (CHead d (Bind Abbr) u)) \to (\forall (t: T).((ty3 g d u t) \to
31 (ty3 g c (TLRef n) (lift (S n) O t))))))))
32 | ty3_abst: \forall (n: nat).(\forall (c: C).(\forall (d: C).(\forall (u:
33 T).((getl n c (CHead d (Bind Abst) u)) \to (\forall (t: T).((ty3 g d u t) \to
34 (ty3 g c (TLRef n) (lift (S n) O u))))))))
35 | ty3_bind: \forall (c: C).(\forall (u: T).(\forall (t: T).((ty3 g c u t) \to
36 (\forall (b: B).(\forall (t1: T).(\forall (t2: T).((ty3 g (CHead c (Bind b)
37 u) t1 t2) \to (\forall (t0: T).((ty3 g (CHead c (Bind b) u) t2 t0) \to (ty3 g
38 c (THead (Bind b) u t1) (THead (Bind b) u t2)))))))))))
39 | ty3_appl: \forall (c: C).(\forall (w: T).(\forall (u: T).((ty3 g c w u) \to
40 (\forall (v: T).(\forall (t: T).((ty3 g c v (THead (Bind Abst) u t)) \to (ty3
41 g c (THead (Flat Appl) w v) (THead (Flat Appl) w (THead (Bind Abst) u
43 | ty3_cast: \forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c t1 t2)
44 \to (\forall (t0: T).((ty3 g c t2 t0) \to (ty3 g c (THead (Flat Cast) t2 t1)
45 (THead (Flat Cast) t0 t2))))))).